Grid-tie voltage source converters (VSCs) can operate in three distinct modes: AC-dominant, DC-dominant, and balanced, depending on the placement of the stiff voltage sources. The varying operation modes of the VSCs traditionally demand different synchronization control techniques, posing challenges for the power systems to accommodate and coordinate the VSCs. A promising universal control technique for VSCs is the DC-link voltage synchronization control (DVSC) based on a lead compensator (LC). The LC DVSC stabilizes both the DC and AC voltages of a VSC while achieving synchronization with the AC grid. This results in a dual-port grid-forming (DGFM) characteristic for the VSC. However, there has been very limited study on the stability and synchronization controller design of the VSCs with the LC DVSC operating in various modes. To bridge this gap, the paper presents a quantitative analysis on the stability and steady-state performance of the LC DVSC in all three operation modes of the DGFM VSC. Based on the analysis, the paper provides step-by-step design guidelines for the LC DVSC. Furthermore, the paper uncovers an instability issue related to the LC DVSC when the DGFM VSC operates in the balanced mode. To tackle the instability issue, a virtual resistance control is proposed and integrated with the LC DVSC. Simulation results validate the analysis and demonstrate the effectiveness of the DGFM VSC with LC DVSC designed using the proposed guidelines in all three operation modes. Overall, the paper demonstrates the feasibility of employing the DGFM VSC with the LC DVSC for all three possible operation modes.